# How do you calculate pressure in a plasma?

1. Aug 23, 2006

### RGClark

A gas has some pressure due to simply its heat. However, if the some or all of the molecules are ionized it will also have some additional pressure due to the Coulomb repulsion of the molecules at the same charge.
How do you calculate the total pressure depending on the proportion of ionized molecules?
Suppose you were able to remove all the electrons from the system that were stripped from molecules that were ionized. Would the result be the same in that case?

Bob Clark

2. Aug 25, 2006

### lalbatros

Bob,

Plasmas are usually "quasi-neutral".
This means that the unbalance between negative ans positive charges is usually very small. This is because any small unbalance lead to huge electrostatic forces.

However, with an unbalance, an electrostatic field may occur in the plasma. This gives rise to the usual electrostatic pressure ED/2. The mechanical balance equation should then include the sum of the "kinetic pressure" and the electrostatic pressure: p + ED/2. The kinetic pressure should be very high since plasma occurs at temperatures above -say- 1eV or 11000K.

As you can see, plasma cannot stay confined if there is not a force to equilibrate the pressure dur to the temperature. Forces by wall cannot be considered usually. Magnetic force are used in laboratories. The equilibrium is obtained by include the magnetic pressure term BH/2.

In plasmas, the temperature of ions and electron are often different. Then, different pressures and equilibrium have to be considered.

In tokamaks, the confinement magnetic field is obtained from a combination of extranl coils and a large current within the plasma itself. Due to the different rate of diffusion of charged species, there is also an electric field that arise, specially in edge of the plasma where tempertare and density gradients are large. This electric field combined with the magnetic configuration can cause a rotation of the plasma.

Have a look at the http://www.jet.efda.org/pages/fusion-basics.html" [Broken] on the Joint European Torus web site.

Michel

Last edited by a moderator: May 2, 2017